O.R. and some French roads

I am always intrigued when I find references to some kind of modelling which is identifiable as O.R. in obscure places. A book on the historical geography of France has provided two such observations. ("The Discovery of France" by Graham Robb)

Writing about the mid nineteenth century, "In the Landes, where carriages sank in the sand up to their axles, the engineer Chambrelent calculated that once a road reached a certain length it would be destroyed by the process that built it: 'In travelling to the point where it will be used to prolong the road, one cubic metre of stone or gravel wears out more than one cubic metre of road.'"
The modelling must have been based on some observations and statistical analysis.

Then, about roads later in the nineteenth century, "The chief engineer in the Limousin, Pierre Tresaguet, had insisted that a limit sould be placed on [road] gradients. ... The old road east of Morlaix still includes a needless climb of 15 per cent (1 in 7) because the blundering military Governor of Brittany, the Duc d'Aiguillon, preferred straight lines to the more accommodating curve of the older road that runs alongside. Thanks in part to Tresaguet, it is unusual now to find a climb in excess of 8 per cent (1 in 12). This was thought to be the steepest gradient that a fully laden mule could manage. British mountain roads seem to rise in fits and starts like step pyramids. French mountain roads go much higher, but more steadily, and can comfortably be climbed for hours by a fully laden cyclist."

So far so good; the road builders were given a constraint which had been thought about in terms of the users of the road. But there's a twist in the footnote to these comments, indicating that other people didn't make observations:

"To judge by the army handbook of 1884, it is fortunate that most road building was left to civil engineers:
Gradient on which troops can still march in good order: 25 per cent;
Gradient manageable by mounted horses and light carriages: 33 per cent;
Gradient manageable by mules: 50 per cent;
Escarpment that an infantryman can still cross by using his hands: 100 per cent (completely vertical)"

Models for hydroelectricity

Last week Tina and I visited the Old Walls Hydro site in Ponsworthy on Dartmoor. Water is taken from the West Webburn river and diverted along a leat to give a 16 metre head of water for two turbines. As a piece of engineering it is fascinating.

Various aspects of the design reminded me of some operational research principles. For parts of the design, the owners were told that what they proposed was impossible. How many times does an O.R. scientist or team meet such prejudice? Too often. Sometimes the problem is posed with a feasible region that is too small, simply because nobody has pushed the limits. Beware of incorrect definitions of feasibility!

Then, there were matters of feedback. One of these concerned filtering the water before it entered the pipes to the turbines. Leaves and other vegetation falls into the leat and is trapped on a wire mesh conveyor belt. Once sensors detect that there is a difference in the level of water before and after this screen, a motor starts and removes a "belt-load" of debris. How should this be powered? The simple answer would be to take the power from the turbines ... but that can be affected by the presence of the debris and could cause the system to collapse. So, the motor is isolated from the hydro power. It runs on a small battery, which of course is then trickle charged from the turbines. The O.R. lesson is that feedback needs to be controlled, so that it gives useful control at all times, and not in ideal conditions.

Optimising a sound system

A curious story came my way, which is a piece of optimisation which has never been (and probably never will be) written up as an academic paper. But that's true of much applied O.R. all the time. Even academics who need to publish find that some of their studies are simply unpublishable. The story came from Dustin Curtis' blog.

He described meeting a sound engineer who set up ambient sound systems for Walt Disney World. Here's an extract:

In the mid 1990’s, the park started researching the problem. It would eventually find no existing solution, so the engineers had to design and construct, on their own, one of the most complex and advanced audio systems ever built. The work paid off: today, as you walk through Disney World, the volume of the ambient music does not change. Ever. More than 15,000 speakers have been positioned using complex algorithms to ensure that the sound plays within a range of just a couple decibels throughout the entire park. It is quite a technical feat acoustically, electrically, and mathematically.

Just think what O.R. tools would be needed for that sort of optimisation and design!